In wireless communications using the Orthogonal Frequency Division Multiplexing (OFDM) system, the receiver estimates the channel using pilot signals. The pilot signals here refer to signals known by both the transmitter and receiver. For example, in a standard for high-speed mobile communications, the Long Term Evolution (LTE), pilot signals are arranged at given intervals both in the frequency direction and in the time direction.
In the case of four transmitting antennas, pilot signals are arranged at intervals of certain subcarriers in each sub-frame according to the LTE transmission format. For example, with regard to the transmitting antennas having the transmitting antenna numbers 0 and 1, pilot signals are arranged at intervals of six subcarriers in the OFDM symbols having the symbol numbers 0, 4, 7, and 11. With regard to the transmitting antennas having the transmitting antenna numbers 2 and 3, pilot signals are arranged at intervals of six subcarriers in OFDM symbols having the symbol numbers 1 and 8.
One known example of such a channel estimation method using pilot signals is a method of obtaining a channel estimation value by both frequency-direction interpolation and time-direction interpolation. Specifically, the receiver estimates the channels of resource elements (REs) where pilot signals are arranged. The receiver then performs frequency-direction interpolation and time-direction interpolation on the channel estimation values of the REs where pilot signals are arranged so as to obtain the channel estimation values of REs where no pilot signals are arranged.
On the other hand, in wireless communication systems (multiple-input multiple-output (MIMO)) using multiple transmitting antennas and receiving antennas, the transmitter precodes signals transmitted by the transmitting antennas so that the receiver may readily divide the transmitted signals.
For example, x′=Px where x represents a yet-to-be-precoded, transmitted signal, P represents a precoding matrix (or vector), and x′ represents a precoded, transmitted signal.
In addition, y=Hx′=HPx where H represents a channel matrix and y represents a received signal. The receiver estimates the channel to obtain a channel estimation value matrix H′ and then de-precodes the channel estimation value matrix to calculate H˜=H′P to obtain an effective channel estimation value matrix H˜. The receiver performs demodulation using the obtained effective channel estimation value matrix H˜.
Hereafter, the channel estimation process and de-precoding process will be described using an example illustrated in FIG. 10. FIG. 10 is a drawing explaining the related art and illustrates the process flow in a case where channel estimation by frequency-direction interpolation, channel estimation by time-direction interpolation, and de-precoding are performed in the presented order so as to obtain the effective channel estimation value corresponding to one sub-frame. Here, it is assumed that four transmitting antennas and one layer are provided according to the LTE transmission format.
As illustrated in FIG. 10, the receiver estimates the channels of REs where pilot signals are arranged. The receiver then performs frequency-direction interpolation using OFDM symbols containing pilot signals so as to obtain the channel estimation values of all the REs in each OFDM symbol.
The receiver then obtains the channel estimation values of symbols between each two OFDM symbols containing pilot signals by time-direction interpolation. Specifically, the receiver obtains the channel estimation values of the symbols having the symbol numbers 0, 4, 7, and 11 of the transmitting antennas having the transmitting antenna numbers 0 and 1 and those of the symbols having the symbol numbers 1 and 8 of the transmitting antennas having the transmitting antenna numbers 2 and 3 by frequency-direction interpolation, and obtains the channel estimation values of the other symbols by linear interpolation.
The channel estimation value after time-direction interpolation is obtained by Formulas (35) and (36) below. In the formulas, a represents a receiving antenna number, b represents a transmitting antenna number, n represents a sub-frame number, t represents a symbol number, and h (a, b, n, t, i) represents the channel estimation value of the subcarrier number i after frequency-direction interpolation. Note that the channel estimation value after the time-direction interpolation is represented by h (a, b, n, t, i) as with the channel estimation value after frequency-direction interpolation. This is because time-direction interpolation is performed with respect to the symbols whose channel estimation value has not been obtained in frequency-direction interpolation.
                              h          ⁡                      (                          a              ,              b              ,              n              ,              t              ,              i                        )                          =                  {                                                                      h                  ⁡                                      (                                          a                      ,                      b                      ,                      n                      ,                      0                      ,                      i                                        )                                                                                                (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      0                                                        )                                                                                                                                                                        4                        -                        t                                            4                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          0                          ,                          i                                                )                                                                              +                                                            t                      4                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          4                          ,                          i                                                )                                                                                                                                          (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      1                                        ,                    2                    ,                    3                                    )                                                                                                      h                  ⁡                                      (                                          a                      ,                      b                      ,                      n                      ,                      4                      ,                      i                                        )                                                                                                (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      4                                                        )                                                                                                                                                                        7                        -                        t                                            3                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          4                          ,                          i                                                )                                                                              +                                                                                    t                        -                        4                                            3                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          7                          ,                          i                                                )                                                                                                                                          (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      5                                        ,                    6                                    )                                                                                                      h                  ⁡                                      (                                          a                      ,                      b                      ,                      n                      ,                      7                      ,                      i                                        )                                                                                                (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      7                                                        )                                                                                                                                                                        11                        -                        t                                            4                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          7                          ,                          i                                                )                                                                              +                                                                                    t                        -                        7                                            4                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          11                          ,                          i                                                )                                                                                                                                          (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      8                                        ,                    9                    ,                    10                                    )                                                                                                      h                  ⁡                                      (                                          a                      ,                      b                      ,                      n                      ,                      11                      ,                      i                                        )                                                                                                (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      11                                                        )                                                                                                                                                                        14                        -                        t                                            3                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          11                          ,                          i                                                )                                                                              +                                                                                    t                        -                        11                                            3                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                                                      n                            +                            1                                                    ,                          0                          ,                          i                                                )                                                                                                                                          (                                                            b                      =                      0                                        ,                    1                    ,                                          t                      =                      12                                        ,                    13                                    )                                                                                        (        35        )                                          h          ⁡                      (                          a              ,              b              ,              n              ,              t              ,              i                        )                          =                  {                                                                                                                1                      7                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                                                      n                            -                            1                                                    ,                          8                          ,                          i                                                )                                                                              +                                                            6                      7                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          1                          ,                          i                                                )                                                                                                                                          (                                                            b                      =                      2                                        ,                    3                    ,                                          t                      =                      0                                                        )                                                                                                      h                  ⁡                                      (                                          a                      ,                      b                      ,                      n                      ,                      1                      ,                      i                                        )                                                                                                (                                                            b                      =                      2                                        ,                    3                    ,                                          t                      =                      1                                                        )                                                                                                                                                                        8                        -                        t                                            7                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          1                          ,                          i                                                )                                                                              +                                                                                    t                        -                        1                                            7                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          8                          ,                          i                                                )                                                                                                                                          (                                                            b                      =                      2                                        ,                    3                    ,                                          t                      =                      2                                        ,                    3                    ,                    …                    ⁢                                                                                  ,                    7                                    )                                                                                                      h                  ⁡                                      (                                          a                      ,                      b                      ,                      n                      ,                      8                      ,                      i                                        )                                                                                                (                                                            b                      =                      2                                        ,                    3                    ,                                          t                      =                      8                                                        )                                                                                                                                                                        15                        -                        t                                            7                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                          n                          ,                          8                          ,                          i                                                )                                                                              +                                                                                    t                        -                        8                                            7                                        ⁢                                          h                      ⁡                                              (                                                  a                          ,                          b                          ,                                                      n                            +                            1                                                    ,                          1                          ,                          i                                                )                                                                                                                                          (                                                            b                      =                      2                                        ,                    3                    ,                                          t                      =                      9                                        ,                    …                    ⁢                                                                                  ,                    13                                    )                                                                                        (        36        )            
Subsequently, as illustrated in FIG. 10, the channel estimation values of the four transmitting antennas are de-precoded to obtain the effective channel estimation value corresponding to one layer. The effective channel estimation value h˜(a, l, n, t, i) after de-precoding where a represents a receiving antenna number, l represents a layer number, n represents a sub-frame number, t represents a symbol number, and i represents a subcarrier number is obtained by Formula (37) below. When Formulas (35) and (36) are substituted into Formula (37), the effective channel estimation values are obtained as indicated by Formulas (38) to (51) below.
                                          h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              t              ,              i                        )                          =                                            V              0                        ⁢                          h              ⁡                              (                                  a                  ,                  0                  ,                  n                  ,                  t                  ,                  i                                )                                              +                                    V              1                        ⁢                          h              ⁡                              (                                  a                  ,                  1                  ,                  n                  ,                  t                  ,                  i                                )                                              +                                    V              2                        ⁢                          h              ⁡                              (                                  a                  ,                  2                  ,                  n                  ,                  t                  ,                  i                                )                                              +                                    V              3                        ⁢                          h              ⁡                              (                                  a                  ,                  3                  ,                  n                  ,                  t                  ,                  i                                )                                                                        (        37        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              0              ,              i                        )                          =                                            V              0                        ⁢                          h              ⁡                              (                                  a                  ,                  0                  ,                  n                  ,                  0                  ,                  i                                )                                              +                                    V              1                        ⁢                          h              ⁡                              (                                  a                  ,                  1                  ,                  n                  ,                  0                  ,                  i                                )                                              +                                    V              2                        ⁡                          (                                                                    1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                                                  n                          -                          1                                                ,                        8                        ,                        i                                            )                                                                      +                                                      6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        1                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                                                  n                          -                          1                                                ,                        8                        ,                        i                                            )                                                                      +                                                      6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        1                        ,                        i                                            )                                                                                  )                                                          (        38        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              1              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        0                        ,                        i                                            )                                                                      +                                                      1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        4                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁡                          (                                                                    3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        0                        ,                        i                                            )                                                                      +                                                      1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        4                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁢                          h              ⁡                              (                                  a                  ,                  2                  ,                  n                  ,                  1                  ,                  i                                )                                              +                                    V              3                        ⁢                          h              ⁡                              (                                  a                  ,                  3                  ,                  n                  ,                  1                  ,                  i                                )                                                                        (        39        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              2              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        0                        ,                        i                                            )                                                                      +                                                      1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        4                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        0                        ,                        i                                            )                                                                      +                                                      1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        4                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                                          (        40        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              3              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        0                        ,                        i                                            )                                                                      +                                                      3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        4                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        0                        ,                        i                                            )                                                                      +                                                      3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        4                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                                          (        41        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              4              ,              i                        )                          =                                            V              0                        ⁢                          h              ⁡                              (                                  a                  ,                  0                  ,                  n                  ,                  4                  ,                  i                                )                                              +                                    V              1                        ⁢                          h              ⁡                              (                                  a                  ,                  1                  ,                  n                  ,                  4                  ,                  i                                )                                              +                                    V              2                        ⁡                          (                                                                    4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                                          (        42        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              5              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        4                        ,                        i                                            )                                                                      +                                                      1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        7                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        4                        ,                        i                                            )                                                                      +                                                      1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        7                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                                          (        43        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              6              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        4                        ,                        i                                            )                                                                      +                                                      2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        7                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        4                        ,                        i                                            )                                                                      +                                                      2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        7                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                                          (        44        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              7              ,              i                        )                          =                                            V              0                        ⁢                          h              ⁡                              (                                  a                  ,                  0                  ,                  n                  ,                  7                  ,                  i                                )                                              +                                    V              1                        ⁢                          h              ⁡                              (                                  a                  ,                  1                  ,                  n                  ,                  7                  ,                  i                                )                                              +                                    V              2                        ⁡                          (                                                                    1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        1                        ,                        i                                            )                                                                      +                                                      6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                                  )                                                          (        45        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              8              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        7                        ,                        i                                            )                                                                      +                                                      1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        11                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        7                        ,                        i                                            )                                                                      +                                                      1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        11                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁢                          h              ⁡                              (                                  a                  ,                  2                  ,                  n                  ,                  8                  ,                  i                                )                                              +                                    V              3                        ⁢                          h              ⁡                              (                                  a                  ,                  3                  ,                  n                  ,                  8                  ,                  i                                )                                                                        (        46        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              9              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        7                        ,                        i                                            )                                                                      +                                                      1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        11                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        7                        ,                        i                                            )                                                                      +                                                      1                    2                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        11                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    6                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      1                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                                          (        47        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              10              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        7                        ,                        i                                            )                                                                      +                                                      3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        11                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    1                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        7                        ,                        i                                            )                                                                      +                                                      3                    4                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        11                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                                          (        48        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              11              ,              i                        )                          =                                            V              0                        ⁢                          h              ⁡                              (                                  a                  ,                  0                  ,                  n                  ,                  11                  ,                  i                                )                                              +                                    V              1                        ⁢                          h              ⁡                              (                                  a                  ,                  1                  ,                  n                  ,                  11                  ,                  i                                )                                              +                                    V              2                        ⁡                          (                                                                    4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                                                  n                          +                          1                                                ,                        8                        ,                        i                                            )                                                                      +                                                      3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                                          (        49        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              12              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        11                        ,                        i                                            )                                                                      +                                                      1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                                                  n                          +                          1                                                ,                        0                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        11                        ,                        i                                            )                                                                      +                                                      1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                                                  n                          +                          1                                                ,                        0                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    3                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      4                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                                          (        50        )                                                      h            ~                    ⁡                      (                          a              ,              0              ,              n              ,              13              ,              i                        )                          =                                            V              0                        ⁡                          (                                                                    1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                        n                        ,                        11                        ,                        i                                            )                                                                      +                                                      2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        0                        ,                                                  n                          +                          1                                                ,                        0                        ,                        i                                            )                                                                                  )                                +                                    V              1                        ⁢                          (                                                                    1                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                        n                        ,                        11                        ,                        i                                            )                                                                      +                                                      2                    3                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        1                        ,                                                  n                          +                          1                                                ,                        0                        ,                        i                                            )                                                                                  )                                +                                    V              2                        ⁡                          (                                                                    2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        2                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                +                                    V              3                        ⁡                          (                                                                    2                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                        n                        ,                        8                        ,                        i                                            )                                                                      +                                                      5                    7                                    ⁢                                      h                    ⁡                                          (                                              a                        ,                        3                        ,                                                  n                          +                          1                                                ,                        1                        ,                        i                                            )                                                                                  )                                                          (        51        )            
Examples of the above-mentioned related art include Japanese Laid-open Patent Publication No. 2008-236428.
Incidentally, for the technology involving the above-mentioned channel estimation and de-precoding processes, the effective channel estimation values are calculated by obtaining the channel estimation values of all the symbols and then performing de-precoding. Unfortunately, this increases the number of symbols to be interpolated in the time direction and the number of symbols to be de-precoded, increasing the complexity, followed by increases in power consumption.